Geostatistics Example
Toy dataset from Blangiardo and Cameletti (2015).
# Plot the data.
plot(s2 ~ s1, col = rgb(SPDEtoy$y / max(SPDEtoy$y), 0, 0), data = SPDEtoy,
pch = 19, asp = 1, main = 'Toy Data')

# Create a mesh for the SPDE method and then plot it.
toy_mesh <- inla.mesh.2d(as.matrix(SPDEtoy[,c('s1', 's2')]),
max.edge = c(0.1, 0.2))
plot(toy_mesh, asp = 1)
points(SPDEtoy$s1, SPDEtoy$s2, col = rgb(SPDEtoy$y / max(SPDEtoy$y), 0, 0, 0.5),
pch = 20)

# SPDE projector matrix for estimation.
A_est <- inla.spde.make.A(toy_mesh, as.matrix(SPDEtoy[,c('s1', 's2')]))
# Initialize exponential covariance structure for SPDE.
spde <- inla.spde2.matern(mesh = toy_mesh, alpha = 2)
# Set up stack for estimation.
stack_index <- inla.spde.make.index(name = 'spatial_field', n.spde = spde$n.spde)
stack_est <- inla.stack(data = list(y = SPDEtoy$y), A = list(A_est), effects = list(c(stack_index, list(intercept = 1))), tag = 'est')
# Create a grid for prediction.
toy_nx <- 50
toy_ny <- 50
toy_grid <- expand.grid(x = seq(0, 1, length.out = toy_nx), y = seq(0, 1, length.out = toy_ny))
# SPDE projector matrix for prediction.
A_pred <- inla.spde.make.A(mesh = toy_mesh, loc = as.matrix(toy_grid))
# Set up stacks for prediction.
stack_latent <- inla.stack(data = list(xi = NA), A = list(A_pred), effects = list(stack_index), tag = 'pred_latent')
stack_response <- inla.stack(data = list(y = NA), A = list(A_pred), effects = list(c(stack_index, list(intercept = 1))), tag = 'pred_response')
# Join all three stacks.
stacks <- inla.stack(stack_est, stack_latent, stack_response)
# Fit the model with INLA.
toy_fit <- inla(
y ~ -1 + intercept + f(spatial_field, model = spde),
data = inla.stack.data(stacks),
control.predictor = list(A = inla.stack.A(stacks), compute = TRUE)
)
# Output posterior summaries.
toy_fit$summary.fixed
toy_fit$summary.hyperpar
# Extract posterior mean of latent spatial field.
index_latent <- inla.stack.index(stacks, tag = 'pred_latent')$data
post_mean <- toy_fit$summary.linear.predictor[index_latent, 'mean']
post_sd <- toy_fit$summary.linear.predictor[index_latent, 'sd']
# Plot the posterior mean and SD of the latent spatial field.
plot(im(matrix(post_mean, nrow = toy_nx, ncol = toy_ny), xrange = range(toy_grid$x), yrange = range(toy_grid$y)), main = 'Posterior Mean of Spatial Field')

plot(im(matrix(post_sd, nrow = toy_nx, ncol = toy_ny), xrange = range(toy_grid$x), yrange = range(toy_grid$y)), main = 'Posterior SD of Spatial Field')

Bei Dataset
Example from Møller and Waagepetersen (2007), Beilschmiedia pendula Lauraceae locations in a plot in Panama. bei dataset in spatstat (Baddeley and Turner 2005).
# Plot the full point pattern.
plot(bei, pch = '.', cols = 'black', main = 'Realized Point Pattern')

bei_corners <- vertices.owin(Window(bei))
bei_domain <- cbind(bei_corners$x, bei_corners$y)
bei_full_mesh <- inla.mesh.2d(cbind(bei$x, bei$y),
cutoff = 50, max.edge = c(50, 100),
loc.domain = bei_domain)
plot(bei_full_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
points(bei, pch = '.', col = 'blue')

bei_full_spdf <- as.SpatialPoints.ppp(bei)
# CHECK PRIORS!
matern_full <- inla.spde2.pcmatern(bei_full_mesh,
prior.sigma = c(0.1, 0.99),
prior.range = c(5, 0.01))
cmp_full <- coordinates ~ mySmooth(map = coordinates, model = matern_full) + Intercept
bei_full_lgcp <- lgcp(cmp_full, bei_full_spdf)
lambda_full <- predict(bei_full_lgcp, pixels(bei_full_mesh), ~ exp(mySmooth + Intercept))
# Plot posterior means and posterior sd.
plot(lambda_full)
plot(Window(bei), border = 'white', add = TRUE)
points(bei, pch = '.', col = 'white')

plot(lambda_full['sd'])
plot(Window(bei), border = 'white', add = TRUE)
points(bei, pch = '.', col = 'white')

# Take a sample of quadrats and plot the observed point pattern.
set.seed(84323)
n_quads <- 10
botleft <- cbind(runif(n_quads, 0, 950), runif(n_quads, 0, 450))
bei_interior <- lapply(seq_len(nrow(botleft)), function(r){return(
cbind(
botleft[r, 1] + c(0, 0, 50, 50),
botleft[r, 2] + c(0, 50, 50, 0)
)
)})
bei_win <- do.call(
union.owin,
apply(botleft, 1, function(x){return(
owin(x[1] + c(0, 50), x[2] + c(0, 50))
)})
)
bei_hole <- bei[complement.owin(bei_win)]
bei_samp <- bei[bei_win]
bei_window_full <- Window(bei)
plot(bei_hole, main = 'Observed Subregion', pch = '.', cols = 'black')

bei_hole_mesh <- inla.mesh.2d(cbind(bei_hole$x, bei_hole$y),
cutoff = 50, max.edge = c(50, 100),
loc.domain = bei_domain)
plot(bei_hole_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
points(bei_hole, pch = '.', col = 'blue')

bei_hole_spdf <- as.SpatialPoints.ppp(bei_hole)
# CHECK PRIORS!
matern_hole <- inla.spde2.pcmatern(bei_hole_mesh,
prior.sigma = c(0.1, 0.99),
prior.range = c(5, 0.01))
cmp_hole <- coordinates ~ mySmooth(map = coordinates, model = matern_hole) + Intercept
bei_hole_lgcp <- lgcp(cmp_hole, bei_hole_spdf)
lambda_hole <- predict(bei_hole_lgcp, pixels(bei_hole_mesh), ~ exp(mySmooth + Intercept))
# Plot posterior means and posterior sd.
plot(lambda_hole)
plot(Window(bei_hole), border = 'white', add = TRUE)
points(bei_hole, pch = '.', col = 'white')

plot(lambda_hole['sd'])
plot(Window(bei_hole), border = 'white', add = TRUE)
points(bei_hole, pch = '.', col = 'white')

plot(bei_window_full, main = 'Observed Sample')
plot(bei_win, add = TRUE)
plot(bei_samp, pch = '.', cols = 'black', add = TRUE)

bei_samp_mesh <- inla.mesh.2d(cbind(bei_samp$x, bei_samp$y),
cutoff = 50, max.edge = c(50, 100),
loc.domain = bei_domain)
plot(bei_samp_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
plot(Window(bei_samp), border = 'blue', add = TRUE)
points(bei_samp, pch = '.', col = 'blue')

bei_samp_spdf <- as.SpatialPoints.ppp(bei_samp)
# CHECK PRIORS!
matern_samp <- inla.spde2.pcmatern(bei_samp_mesh,
prior.sigma = c(0.1, 0.99),
prior.range = c(5, 0.01))
cmp_samp <- coordinates ~ mySmooth(map = coordinates, model = matern_samp) + Intercept
bei_samp_lgcp <- lgcp(cmp_samp, bei_samp_spdf)
lambda_samp <- predict(bei_samp_lgcp, pixels(bei_samp_mesh), ~ exp(mySmooth + Intercept))
# Plot posterior means and posterior sd.
plot(lambda_samp)
plot(Window(bei), border = 'white', add = TRUE)
plot(Window(bei_samp), border = 'white', add = TRUE)
points(bei_samp, pch = '.', col = 'white')

plot(lambda_samp['sd'])
plot(Window(bei), border = 'white', add = TRUE)
plot(Window(bei_samp), border = 'white', add = TRUE)
points(bei_samp, pch = '.', col = 'white')

---
title: "Spatial Prediction with INLA"
author: "Kenneth A. Flagg"
bibliography: "../references.bib"
output:
  html_notebook:
    fig_height: 6
    fig_width: 10
    fig_crop: FALSE
    height: "960px"
    width: "720px"
    self_contained: TRUE
---


```{r setup, cache = FALSE, echo = FALSE, message = FALSE, warning = FALSE}
knitr::opts_chunk$set(cache = FALSE, echo = TRUE, warning = FALSE,
  message = FALSE, dpi = 150, fig.align = 'center')
```

```{r packages, cache = FALSE, echo = FALSE, message = FALSE, warning = FALSE}
library(spatstat)
library(INLA)
library(inlabru)
library(maptools)
```


# Introduction

This vignette illustrates the use of INLA for spatial prediction using examples
from @rinla and @illianetal. For prediction of continuous spatial processes,
the stochastic partial differential equations (SPDE) approach is used to
approximate the process through an areal Gaussian Markov random field (GMRF)
representation.


# GMRF Background

@rinla section 6.1.

- Observations aggregated to disjoint areal regions indexed by $i$.
- Each region has unique parameter $\theta_{i}$.
- $\mathcal{N}(i)$ is the set of indices of neighbors of region $i$ and
  $\mathcal{N}_{i} = |\mathcal{N}(i)|$ is the number of neighbor of region $i$.
- Local Markov property: given $\boldsymbol{\theta}_{\mathcal{N}(i)}$,
  $\theta_{i}$ is independent of all other $\theta_{j}$.
- Then the precision matrix $\mathbf{Q}$ of $\boldsymbol{\theta}$ is sparse
  because only neighbors have nonzero coprecisions.

- Besag-York-Molli&#x00e8; model:
    - Exchangeable random effects $u_{i}$ with intrinsic conditional
      autoregressive (iCAR) structure.
    - $u_{i}|\mathbf{u}_{-i} \sim \mathrm{N}\left(\mu_{i} + \sum_{j} a_{ij} (u_{j} - \mu_{j}) / \mathcal{N}_{i}, \sigma_{u}^{2} / \mathcal{N}_{i}\right)$
    - (What are the $a_{ij}?$).
    - iCAR is an improper prior because covariance matrix not positive definite
      but this is ok for random effects.


# SPDE Background

*Find Lindgren et. al. (2011) and fill in motivation*

- Spatial process $\xi(\mathbf{s})$.

- Solve $(\kappa^{2} - \Delta)^{\alpha / 2}(\tau \xi(\mathbf{s})) = \mathcal{W}(\mathbf{s})$.
    - $\kappa$ is a range parameter.
    - $\Delta$ is the Laplacian.
    - $\alpha$ is a smoothness parameter.
    - $\tau$ a precision parameter.
    - Exact and sationary solution: $\xi(\mathbf{s})$ is a Gaussian field with Mat&#x00e8;rn covariance function.

- Finite element approximation $$.


# Geostatistics Example

Toy dataset from @rinla.

```{r spdetoy, fig.width = 6, out.width = '60%'}
# Plot the data.
plot(s2 ~ s1, col = rgb(SPDEtoy$y / max(SPDEtoy$y), 0, 0), data = SPDEtoy,
     pch = 19, asp = 1, main = 'Toy Data')
```

```{r spdemesh, fig.width = 6, out.width = '60%'}
# Create a mesh for the SPDE method and then plot it.
toy_mesh <- inla.mesh.2d(as.matrix(SPDEtoy[,c('s1', 's2')]),
                         max.edge = c(0.1, 0.2))
plot(toy_mesh, asp = 1)
points(SPDEtoy$s1, SPDEtoy$s2, col = rgb(SPDEtoy$y / max(SPDEtoy$y), 0, 0, 0.5),
       pch = 20)
```

```{r spdefit}
# SPDE projector matrix for estimation.
A_est <- inla.spde.make.A(toy_mesh, as.matrix(SPDEtoy[,c('s1', 's2')]))

# Initialize exponential covariance structure for SPDE.
spde <- inla.spde2.matern(mesh = toy_mesh, alpha = 2)

# Set up stack for estimation.
stack_index <- inla.spde.make.index(name = 'spatial_field', n.spde = spde$n.spde)
stack_est <- inla.stack(data = list(y = SPDEtoy$y), A = list(A_est), effects = list(c(stack_index, list(intercept = 1))), tag = 'est')

# Create a grid for prediction.
toy_nx <- 50
toy_ny <- 50
toy_grid <- expand.grid(x = seq(0, 1, length.out = toy_nx), y = seq(0, 1, length.out = toy_ny))

# SPDE projector matrix for prediction.
A_pred <- inla.spde.make.A(mesh = toy_mesh, loc = as.matrix(toy_grid))

# Set up stacks for prediction.
stack_latent <- inla.stack(data = list(xi = NA), A = list(A_pred), effects = list(stack_index), tag = 'pred_latent')
stack_response <- inla.stack(data = list(y = NA), A = list(A_pred), effects = list(c(stack_index, list(intercept = 1))), tag = 'pred_response')

# Join all three stacks.
stacks <- inla.stack(stack_est, stack_latent, stack_response)

# Fit the model with INLA.
toy_fit <- inla(
  y ~ -1 + intercept + f(spatial_field, model = spde),
  data = inla.stack.data(stacks),
  control.predictor = list(A = inla.stack.A(stacks), compute = TRUE)
)

# Output posterior summaries.
toy_fit$summary.fixed
toy_fit$summary.hyperpar

# Extract posterior mean of latent spatial field.
index_latent <- inla.stack.index(stacks, tag = 'pred_latent')$data
post_mean <- toy_fit$summary.linear.predictor[index_latent, 'mean']
post_sd <- toy_fit$summary.linear.predictor[index_latent, 'sd']

# Plot the posterior mean and SD of the latent spatial field.
plot(im(matrix(post_mean, nrow = toy_nx, ncol = toy_ny), xrange = range(toy_grid$x), yrange = range(toy_grid$y)), main = 'Posterior Mean of Spatial Field')
plot(im(matrix(post_sd, nrow = toy_nx, ncol = toy_ny), xrange = range(toy_grid$x), yrange = range(toy_grid$y)), main = 'Posterior SD of Spatial Field')
```


# Bei Dataset

Example from @moellerwaagepetersen, _Beilschmiedia pendula Lauraceae_ locations
in a plot in Panama. `bei` dataset in `spatstat` [@spatstat].

```{r beipts}
# Plot the full point pattern.
plot(bei, pch = '.', cols = 'black', main = 'Realized Point Pattern')
```

```{r beimesh}
bei_corners <- vertices.owin(Window(bei))
bei_domain <- cbind(bei_corners$x, bei_corners$y)
bei_full_mesh <- inla.mesh.2d(cbind(bei$x, bei$y),
                              cutoff = 50, max.edge = c(50, 100),
                              loc.domain = bei_domain)
plot(bei_full_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
points(bei, pch = '.', col = 'blue')
```

```{r beifulllgcp, cache = TRUE}
bei_full_spdf <- as.SpatialPoints.ppp(bei)
# CHECK PRIORS!
matern_full <- inla.spde2.pcmatern(bei_full_mesh,
                                   prior.sigma = c(0.1, 0.99),
                                   prior.range = c(5, 0.01))
cmp_full <- coordinates ~ mySmooth(map = coordinates, model = matern_full) + Intercept
bei_full_lgcp <- lgcp(cmp_full, bei_full_spdf)
lambda_full <- predict(bei_full_lgcp, pixels(bei_full_mesh), ~ exp(mySmooth + Intercept))

# Plot posterior means and posterior sd.
plot(lambda_full)
plot(Window(bei), border = 'white', add = TRUE)
points(bei, pch = '.', col = 'white')
plot(lambda_full['sd'])
plot(Window(bei), border = 'white', add = TRUE)
points(bei, pch = '.', col = 'white')
```

```{r beihole}
# Take a sample of quadrats and plot the observed point pattern.
set.seed(84323)
n_quads <- 10
botleft <- cbind(runif(n_quads, 0, 950), runif(n_quads, 0, 450))
bei_interior <- lapply(seq_len(nrow(botleft)), function(r){return(
    cbind(
      botleft[r, 1] + c(0, 0, 50, 50),
      botleft[r, 2] + c(0, 50, 50, 0)
    )
  )})
bei_win <- do.call(
  union.owin,
  apply(botleft, 1, function(x){return(
    owin(x[1] + c(0, 50), x[2] + c(0, 50))
  )})
)
bei_hole <- bei[complement.owin(bei_win)]
bei_samp <- bei[bei_win]
bei_window_full <- Window(bei)

plot(bei_hole, main = 'Observed Subregion', pch = '.', cols = 'black')
```

```{r beiholemesh}
bei_hole_mesh <- inla.mesh.2d(cbind(bei_hole$x, bei_hole$y),
                              cutoff = 50, max.edge = c(50, 100),
                              loc.domain = bei_domain)
plot(bei_hole_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
points(bei_hole, pch = '.', col = 'blue')
```

```{r beiholelgcp, cache = TRUE}
bei_hole_spdf <- as.SpatialPoints.ppp(bei_hole)
# CHECK PRIORS!
matern_hole <- inla.spde2.pcmatern(bei_hole_mesh,
                                   prior.sigma = c(0.1, 0.99),
                                   prior.range = c(5, 0.01))
cmp_hole <- coordinates ~ mySmooth(map = coordinates, model = matern_hole) + Intercept
bei_hole_lgcp <- lgcp(cmp_hole, bei_hole_spdf)
lambda_hole <- predict(bei_hole_lgcp, pixels(bei_hole_mesh), ~ exp(mySmooth + Intercept))

# Plot posterior means and posterior sd.
plot(lambda_hole)
plot(Window(bei_hole), border = 'white', add = TRUE)
points(bei_hole, pch = '.', col = 'white')
plot(lambda_hole['sd'])
plot(Window(bei_hole), border = 'white', add = TRUE)
points(bei_hole, pch = '.', col = 'white')
```

```{r beisamp}
plot(bei_window_full, main = 'Observed Sample')
plot(bei_win, add = TRUE)
plot(bei_samp, pch = '.', cols = 'black', add = TRUE)
```

```{r beisampmesh}
bei_samp_mesh <- inla.mesh.2d(cbind(bei_samp$x, bei_samp$y),
                              cutoff = 50, max.edge = c(50, 100),
                              loc.domain = bei_domain)
plot(bei_samp_mesh, asp = 1)
plot(Window(bei), border = 'blue', add = TRUE)
plot(Window(bei_samp), border = 'blue', add = TRUE)
points(bei_samp, pch = '.', col = 'blue')
```

```{r beisamplgcp, cache = TRUE}
bei_samp_spdf <- as.SpatialPoints.ppp(bei_samp)
# CHECK PRIORS!
matern_samp <- inla.spde2.pcmatern(bei_samp_mesh,
                                   prior.sigma = c(0.1, 0.99),
                                   prior.range = c(5, 0.01))
cmp_samp <- coordinates ~ mySmooth(map = coordinates, model = matern_samp) + Intercept
bei_samp_lgcp <- lgcp(cmp_samp, bei_samp_spdf)
lambda_samp <- predict(bei_samp_lgcp, pixels(bei_samp_mesh), ~ exp(mySmooth + Intercept))

# Plot posterior means and posterior sd.
plot(lambda_samp)
plot(Window(bei), border = 'white', add = TRUE)
plot(Window(bei_samp), border = 'white', add = TRUE)
points(bei_samp, pch = '.', col = 'white')
plot(lambda_samp['sd'])
plot(Window(bei), border = 'white', add = TRUE)
plot(Window(bei_samp), border = 'white', add = TRUE)
points(bei_samp, pch = '.', col = 'white')
```


# References

